1/(1×3×5) +1/(3×5×7)+1/(5×7×9)+…+1/(11×13×15)这个式子怎么用简便运算
来源:百度知道 编辑:UC知道 时间:2024/09/21 23:34:35
1/(1×3×5) +1/(3×5×7)+1/(5×7×9)+…+1/(11×13×15)
=1/2x[1/1x3-1/3x5]+1/2[1/3x5-1/5x7]+....+1/2[1/11x13-1/13x15]
=1/2[1/1x3-1/3x5+1/3x5-1/5x7+....+1/11x13-1/13x15]
=1/2x[1/1x3-1/13x15]
=1/2x64/195
=32/195
上面这位兄弟解法是对的,就是倍数弄错了。。。。
1/(1×3×5) +1/(3×5×7)+1/(5×7×9)+…+1/(11×13×15)
=(1/4)×[1/(1×3)-1/(3×5)]+(1/4)×[1/(3×5)-1/(5×7)]+....+(1/4)×[1/(11×13)-1/(13×15)]
=(1/4)×[1/(1×3)-1/(3×5)+1/(3×5)-1/(5×7)+....+1/(11×13)-1/(13×15)]
=(1/4)×[1/(1×3)-1/(13×15)]
=(1/4)×(64/195)
=16/195
把通项1/(a×b×c)改写成(1/a-2/b+1/c)/8,然后中间的项可以加减抵消掉,只需计算两端的若干个分数的运算即可。
1/(1×3×5) +1/(3×5×7)+…+1/(11×13×15)
=(1/1-2/3+1/5)/8+(1/3-2/5+1/7)/8+...+(1/11-2/13+1/15)/8
=(1/1-2/3+1/5+1/3-2/5+1/7+...+1/11-2/13+1/15)/8
=(2/3-1/13+1/15)/8
=16/195
不知大家有无更好的方法。
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
1/1*3+1/3*5+1/5*7+........+1/17+19
1/1+1/3+1/5+.................+1/(2n-1)=?
1+1/3+1/5+1/7+......1/(2n-1)=?
1/2+1/3+1/4+1/5+.......+1/10
1/2+1/3+1/4+1/5+...+1/100
1/2+1/3+1/4+1/5******+1/2004=?
1/2×1/3×1/4×1/5×…×1/2008
1/1*3+1/2*4+1/3*5+...+1/48*50
1/1*3+1/2*4+1/3*5+......+1/2005*2007